PWM to discrete on\off

Hello,

So here is my problem; I want to power some accessories of the interior lights in my truck. The problem is that the interior lights donít just turn on and off...they turn on normally but when they turn off they fade out (dim). I suspect (but am not sure) that the lights are actually powered by a PWM signal (rather than a simple on\off) and when going out the BCM simply modifies the duty cycle of the PWM signal to affect the fade to black. This means that when I connect my accessories through a relay the relay simply starts buzzing when the lights are going out.

So here is the question...How do I create a simple discrete on\off from the PWM signal?

Actually, the "accessories" are basicly puddle lamps. What I am trying to do is power the lights on the ends of my running boards. Powering them directly from the dome light wires apparently puts to much load on the PWM circuitry beacuse the lights on the running boards and the dome lights quit working at all when the running board lights are directly connected.

Thanks,
Steve

BTW, the vehicle I am working on is a 2011 Ford Super Duty truck. The running boards are factory OEM boards that came from a different truck. The wire I am trying to use to power the board lights is the wire the Ford wiring diagram says is used to power them when they are factory installed. As to why it doesn't work, all I can figure is that the circuitry is beefier in trucks that actually had these boards from the factory??

Although I can figure out some simple electronic stuff, when you start talking about MOSFET and transistors I get lost pretty quickly. Can you be more descriptive about the circuit you are envisioning?

Another question, how can I tell whether the dimming is signal is an analog one or is in fact a PWM? When I measure the voltage, I measure ~12 volts when the door is opened. When the door is closed and after the delay (about 30 seconds) the voltage drops to ~8.5. The voltage stays there for 9 minutes and 30 seconds at which point it drops to ~0. The drop from 12 volts to 8.5 is somewhat gradual causing the dimming effect. However the drop from 8.5 to 0 is nearly instant. Having said all of that, how can I know whether the voltage is droping via analog control or if it is just an effect of my RMS meter reading a PWM signal with a decreasing duty cycle?